|\^/| Maple 18 (X86 64 LINUX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2014 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. [&x, *, +, -, ., <,>, <|>, About, AddCoordinates, ArcLength, BasisFormat, Binormal, Compatibility, ConvertVector, CrossProduct, Curl, Curvature, D, Del, DirectionalDiff, Divergence, DotProduct, Flux, GetCoordinateParameters, GetCoordinates, GetNames, GetPVDescription, GetRootPoint, GetSpace, Gradient, Hessian, IsPositionVector, IsRootedVector, IsVectorField, Jacobian, Laplacian, LineInt, MapToBasis, Nabla, Norm, Normalize, PathInt, PlotPositionVector, PlotVector, PositionVector, PrincipalNormal, RadiusOfCurvature, RootedVector, ScalarPotential, SetCoordinateParameters, SetCoordinates, SpaceCurve, SurfaceInt, TNBFrame, Tangent, TangentLine, TangentPlane, TangentVector, Torsion, Vector, VectorField, VectorPotential, VectorSpace, Wronskian, diff, eval, evalVF, int, limit, series] Path set to /dsk/l1/fgb/13379/FGblib/../libfgbunid.so FGb/Maple interface package Version 1.63 JC Faugere (Jean-Charles.Faugere@inria.fr) Type ?FGb for documentation Warning, `n` is implicitly declared local to procedure `FGbRationalParametrization` Warning, `EQUS` is implicitly declared local to procedure `FGbRationalParametrization` Warning, `linear` is implicitly declared local to procedure `FGbRationalParametrization` Warning, `var` is implicitly declared local to procedure `FGbRationalParametrization` Warning, `S` is implicitly declared local to procedure `FGbRationalParametrization` Warning, `par` is implicitly declared local to procedure `FGbRationalParametrization` Warning, `ls` is implicitly declared local to procedure `FGbRationalParametrization` Warning, `myrand1` is implicitly declared local to procedure `FGbRationalParametrization` Warning, `myrand` is implicitly declared local to procedure `FGbRationalParametrization` Warning, `myprime` is implicitly declared local to procedure `FGbRationalParametrization` Warning, `gb` is implicitly declared local to procedure `FGbRationalParametrization` Warning, `rr1` is implicitly declared local to procedure `FGbRationalParametrization` Warning, `DEG` is implicitly declared local to procedure `FGbRationalParametrization` Warning, `boo` is implicitly declared local to procedure `FGbRationalParametrization` Warning, `i` is implicitly declared local to procedure `FGbRationalParametrization` Warning, `NEWVARS` is implicitly declared local to procedure `FGbRationalParametrization` Warning, `LS` is implicitly declared local to procedure `FGbRationalParametrization` Warning, `param` is implicitly declared local to procedure `FGbRationalParametrization` FGbRationalParametrization := proc(EQUATIONS, VARS) local n, EQUS, linear, var, S, par, ls, myrand1, myrand, myprime, gb, rr1, DEG, boo, i, NEWVARS, LS, param; n := nops(VARS); EQUS := expand(EQUATIONS); if indets(VARS) <> indets(EQUS) then print(indets(EQUS) <> indets(VARS)); error "Variables do not match" end if; if n = 1 then error "Univariate Case" end if; if member(1, map(degree, EQUS)) then linear := map(_pol -> if degree(_pol) = 1 then _pol end if, EQUS); var := indets(linear[1])[1]; S := solve(linear[1], var); par, ls := FGbRationalParametrization(subs(var = S, EQUATIONS), remove(member, VARS, [var])); return par, {op(ls), var = S} end if; myrand1 := rand(1 .. 10); myrand := rand(9000 .. 65519); myprime := nextprime(myrand()); gb := FGb:-fgb_gbasis_lm([VectorCalculus:-`+`( add(VectorCalculus:-`*`(myrand(), VARS[i]), i = 1 .. n), myrand()), op(EQUS)], myprime, [], VARS, {"index" = 99886600, "verb" = 0}); if gb[1] <> [1] then printf("\t\n\n Positive dimension \n\n"); error "Positive dimension" end if; gb := FGb:-fgb_gbasis(EQUS, myprime, [], VARS, {"index" = 99886600, "verb" = 0}); if member(1, map(degree, gb)) then FGb:-fgb_gbasis(EQUS, 0, [], VARS, {"index" = 99886600, "verb" = 0}) ; return [1], {}; error "There is a linear polynomial in the Gb" end if; if gb = [1] then return [seq(1, i = 1 .. nops(vars))], {} end if; rr1 := FGb:-fgb_matrixn(subs(VARS[n] = VectorCalculus:-`+`(add( VectorCalculus:-`*`(myrand(), VARS[i]), i = 1 .. VectorCalculus:-`+`(n, -1)), VARS[n]), gb), myprime, VARS, {"index" = 99886600, "verb" = 0}); if 1 <= nops(map(_sqr -> if 1 < _sqr[2] then _sqr[2] end if, (Sqrfree(rr1[nops(rr1)]) mod myprime)[2])) then printf("Non radical case\n", degree(rr1[nops(rr1)]), add( degree(_pol[1]), _pol in (Sqrfree(rr1[nops(rr1)]) mod myprime)[2])); error "Non radical case" end if; DEG := degree(rr1[nops(rr1)]); printf("\n\nDegree is %d\n\n", DEG); boo := false; for i from nops(VARS) by -1 to 1 do NEWVARS := [op(remove(member, VARS, VARS[i .. i])), VARS[i]]; try rr1 := FGb:-fgb_matrixn(gb, myprime, NEWVARS, {"index" = 99886600, "verb" = 0}); if 0 < nops(rr1) then boo := true; break end if catch: end try end do; if boo then LS := {}; if 0 = 0 then param := FGb:-fgb_matrixn(EQUS, 0, NEWVARS, {"index" = 99886600, "verb" = 0}) else param := FGb:-fgb_matrixn(EQUS, 65521, NEWVARS, {"index" = 99886600, "verb" = 0}) end if else printf("\n\nChange of variables requested\n\n"); LS := {VARS[n] = VectorCalculus:-`+`(VARS[n], add(VectorCalculus:-`*`(myrand1(), VARS[i]), i = 1 .. n))}; if 0 = 0 then param := FGb:-fgb_matrixn( map(expand, subs(LS, EQUS)), 0, VARS, {"index" = 99886600, "verb" = 0}) else param := FGb:-fgb_matrixn(map(expand, subs(LS, EQUS)), 65521, VARS, {"index" = 99886600, "verb" = 0}) end if end if; return param, LS end proc MyIsolation := proc(rrform) local newrr, elimvars, othervars, reg, SOLS, vars, DEG; elimvars := indets(rrform[1])[1]; othervars := map(_eqs -> indets(_eqs) minus {elimvars}, rrform[2 .. nops(rrform)]); othervars := map(_v -> _v[1], othervars); DEG := degree(rrform[1]); newrr := [rrform[1], VectorCalculus:-diff(rrform[1], elimvars), [rem( VectorCalculus:-`*`(VectorCalculus:-diff(rrform[1], elimvars), elimvars), rrform[1], elimvars), seq(VectorCalculus:-`-`( VectorCalculus:-`*`( coeff(rrform[i], othervars[VectorCalculus:-`+`(i, -1)], 0), DEG)), i = 2 .. nops(rrform))]]; reg := lcm(op(map(denom, newrr[3])), denom(newrr[2])); newrr := [numer(newrr[1]), expand(VectorCalculus:-`*`(reg, newrr[2])), map(_eqs -> expand(VectorCalculus:-`*`(_eqs, reg)), newrr[3])]; SOLS := fgbrs:-rs_isolate_rur(newrr[1], newrr[2], newrr[3], elimvars, verbose = 0); vars := [elimvars, op(othervars)]; SOLS := map(_point -> [seq(vars[i] = VectorCalculus:-`*`( VectorCalculus:-`+`(_point[i][1], _point[i][2]), 1/2), i = 1 .. nops(vars))], SOLS); return SOLS end proc my_rs_rur_sys := proc( sys::depends(list(polynom(integer, vars))), vars::list(name), v::name := _Z , {constraints := [], fulloutput::boolean := false, noresult::boolean := false, sepvector::list(integer) := [], useblockingerror::boolean := FAIL, verbose::nonnegint := 0}, $) fgbrs:-rs_rur_gb( fgbrs:-rs_gbasis(sys, vars, ':-useblockingerror' = useblockingerror), vars, v, ':-constraints' = constraints, ':-verbose' = verbose, ':-noresult' = noresult, ':-sepvector' = sepvector, ':-fulloutput' = fulloutput, ':-useblockingerror' = useblockingerror) end proc > read "load.mpl": Warning, `X` is implicitly declared local to procedure `MyRand` Warning, `S` is implicitly declared local to procedure `LittleRankPosDef` Warning, `i` is implicitly declared local to procedure `LittleRankPosDef` Warning, `v` is implicitly declared local to procedure `LittleRankPosDef` Warning, `j` is implicitly declared local to procedure `LittleRankPosDef` Warning, `S` is implicitly declared local to procedure `Deformation` Warning, `i` is implicitly declared local to procedure `Deformation` Warning, `j` is implicitly declared local to procedure `Deformation` Warning, `one` is implicitly declared local to procedure `MyRand2` Warning, `two` is implicitly declared local to procedure `MyRand2` Warning, `rr2` is implicitly declared local to procedure `MyRand2` Warning, `i` is implicitly declared local to procedure `RowElementaryOperation` Warning, `lambda` is implicitly declared local to procedure `RowElementaryOperation` Warning, `j` is implicitly declared local to procedure `RowElementaryOperation` Warning, `i` is implicitly declared local to procedure `ColumnElementaryOperation` Warning, `j` is implicitly declared local to procedure `ColumnElementaryOperation` Warning, `lambda` is implicitly declared local to procedure `ColumnElementaryOperation` Warning, `r` is implicitly declared local to procedure `ApplyAffineTransf` Warning, `c` is implicitly declared local to procedure `ApplyAffineTransf` Warning, `out` is implicitly declared local to procedure `LinearChangeOfVariables` Warning, `t` is implicitly declared local to procedure `LinearChangeOfVariables` Warning, `r` is implicitly declared local to procedure `MakeTriangular` Warning, `c` is implicitly declared local to procedure `MakeTriangular` Warning, `out` is implicitly declared local to procedure `MakeTriangular` Warning, `i` is implicitly declared local to procedure `MakeTriangular` Warning, `j` is implicitly declared local to procedure `MakeTriangular` Warning, `J` is implicitly declared local to procedure `RandomSymmMatrix` Warning, `var` is implicitly declared local to procedure `RandomLinearMatrix` Warning, `M` is implicitly declared local to procedure `RandomLinearMatrix` Warning, `s` is implicitly declared local to procedure `RandomLinearMatrix` Warning, `t` is implicitly declared local to procedure `RandomLinearMatrix` Warning, `var` is implicitly declared local to procedure `RandomSymmetricLinearMatrix` Warning, `M` is implicitly declared local to procedure `RandomSymmetricLinearMatrix` Warning, `s` is implicitly declared local to procedure `RandomSymmetricLinearMatrix` Warning, `t` is implicitly declared local to procedure `RandomSymmetricLinearMatrix` Warning, `vec` is implicitly declared local to procedure `Vectorize` Warning, `i` is implicitly declared local to procedure `Vectorize` Warning, `j` is implicitly declared local to procedure `Vectorize` Warning, `MIN` is implicitly declared local to procedure `SetOfSubMatrices` Warning, `j` is implicitly declared local to procedure `SetOfSubMatrices` Warning, `l` is implicitly declared local to procedure `SetOfSubMatrices` Warning, `listofsubmatrices` is implicitly declared local to procedure `SetOfSubMatrices` Warning, `MIN` is implicitly declared local to procedure `Minors` Warning, `j` is implicitly declared local to procedure `Minors` Warning, `l` is implicitly declared local to procedure `Minors` Warning, `listofminors` is implicitly declared local to procedure `Minors` Warning, `e` is implicitly declared local to procedure `MaxMinorsJacobian` Warning, `v` is implicitly declared local to procedure `MaxMinorsJacobian` Warning, `lv` is implicitly declared local to procedure `MaxMinorsJacobian` Warning, `ld` is implicitly declared local to procedure `MaxMinorsJacobian` Warning, `eqs` is implicitly declared local to procedure `SingularLocus` Warning, `var` is implicitly declared local to procedure `SingularLocus` Warning, `n` is implicitly declared local to procedure `SingularLocus` Warning, `out` is implicitly declared local to procedure `SingularLocus` Warning, `Mat` is implicitly declared local to procedure `MatrixCombination` Warning, `var` is implicitly declared local to procedure `ComputeDimension` Warning, `n` is implicitly declared local to procedure `ComputeDimension` Warning, `eqs` is implicitly declared local to procedure `ComputeDimension` Warning, `GB` is implicitly declared local to procedure `ComputeDimension` Warning, `d` is implicitly declared local to procedure `ComputeDimension` Warning, `var` is implicitly declared local to procedure `ComputeCodimension` Warning, `var` is implicitly declared local to procedure `ComputeDegree` Warning, `eqs` is implicitly declared local to procedure `ComputeDegree` Warning, `dimen` is implicitly declared local to procedure `ComputeDegree` Warning, `i` is implicitly declared local to procedure `ComputeDegree` Warning, `eqs` is implicitly declared local to procedure `EliminateRelations` Warning, `e` is implicitly declared local to procedure `EliminateRelations` Warning, `var` is implicitly declared local to procedure `EliminateRelations` Warning, `v` is implicitly declared local to procedure `EliminateRelations` Warning, `dim` is implicitly declared local to procedure `EliminateRelations` Warning, `cod` is implicitly declared local to procedure `EliminateRelations` Warning, `neweqs` is implicitly declared local to procedure `EliminateRelations` Warning, `i` is implicitly declared local to procedure `EliminateRelations` Warning, `eqs` is implicitly declared local to procedure `EliminateRelationsKnowingCodimension` Warning, `e` is implicitly declared local to procedure `EliminateRelationsKnowingCodimension` Warning, `var` is implicitly declared local to procedure `EliminateRelationsKnowingCodimension` Warning, `v` is implicitly declared local to procedure `EliminateRelationsKnowingCodimension` Warning, `neweqs` is implicitly declared local to procedure `EliminateRelationsKnowingCodimension` Warning, `i` is implicitly declared local to procedure `EliminateRelationsKnowingCodimension` Warning, `vars` is implicitly declared local to procedure `TestTheMembership` Warning, `pol` is implicitly declared local to procedure `TestTheMembership` Warning, `listofpol` is implicitly declared local to procedure `TestTheMembership` Warning, `newlist` is implicitly declared local to procedure `TestTheMembership` Warning, `GB1` is implicitly declared local to procedure `TestTheMembership` Warning, `GB2` is implicitly declared local to procedure `TestTheMembership` Warning, `vars` is implicitly declared local to procedure `TestTheEquality` Warning, `GB1` is implicitly declared local to procedure `TestTheEquality` Warning, `GB2` is implicitly declared local to procedure `TestTheEquality` Warning, `vars` is implicitly declared local to procedure `TestTheInclusion` Warning, `newlist` is implicitly declared local to procedure `TestTheInclusion` Warning, `GB1` is implicitly declared local to procedure `TestTheInclusion` Warning, `GB2` is implicitly declared local to procedure `TestTheInclusion` Warning, `vars` is implicitly declared local to procedure `TestSingularity` Warning, `ss` is implicitly declared local to procedure `TestSingularity` Warning, `GB` is implicitly declared local to procedure `TestSingularity` Warning, `out` is implicitly declared local to procedure `ChangeLines` Warning, `r` is implicitly declared local to procedure `ChangeLines` Warning, `c` is implicitly declared local to procedure `ChangeLines` Warning, `j` is implicitly declared local to procedure `ChangeLines` Warning, `ch` is implicitly declared local to procedure `ChangeLines` Warning, `out` is implicitly declared local to procedure `ChangeColumns` Warning, `r` is implicitly declared local to procedure `ChangeColumns` Warning, `c` is implicitly declared local to procedure `ChangeColumns` Warning, `i` is implicitly declared local to procedure `ChangeColumns` Warning, `ch` is implicitly declared local to procedure `ChangeColumns` Warning, `linear` is implicitly declared local to procedure `FGbRationalParametrizationBiLinear` Warning, `newset` is implicitly declared local to procedure `FGbRationalParametrizationBiLinear` Warning, `var` is implicitly declared local to procedure `FGbRationalParametrizationBiLinear` Warning, `S` is implicitly declared local to procedure `FGbRationalParametrizationBiLinear` Warning, `par` is implicitly declared local to procedure `FGbRationalParametrizationBiLinear` Warning, `ls` is implicitly declared local to procedure `FGbRationalParametrizationBiLinear` Warning, `i` is implicitly declared local to procedure `FGbRationalParametrizationBiLinear` Warning, `NEWVARS` is implicitly declared local to procedure `FGbRationalParametrizationBiLinear` Warning, `LS` is implicitly declared local to procedure `FGbRationalParametrizationBiLinear` Warning, `param` is implicitly declared local to procedure `FGbRationalParametrizationBiLinear` Warning, `NEWINDEX` is implicitly declared local to procedure `FGbRationalParametrizationBiLinear` Warning, `NEWEQS` is implicitly declared local to procedure `FGbRationalParametrizationBiLinear` Warning, `fd` is implicitly declared local to procedure `FGbRationalParametrizationBiLinear` Warning, `n` is implicitly declared local to procedure `MyFGbRationalParametrization` Warning, `EQUS` is implicitly declared local to procedure `MyFGbRationalParametrization` Warning, `linear` is implicitly declared local to procedure `MyFGbRationalParametrization` Warning, `var` is implicitly declared local to procedure `MyFGbRationalParametrization` Warning, `S` is implicitly declared local to procedure `MyFGbRationalParametrization` Warning, `par` is implicitly declared local to procedure `MyFGbRationalParametrization` Warning, `ls` is implicitly declared local to procedure `MyFGbRationalParametrization` Warning, `myrand1` is implicitly declared local to procedure `MyFGbRationalParametrization` Warning, `myrand` is implicitly declared local to procedure `MyFGbRationalParametrization` Warning, `myprime` is implicitly declared local to procedure `MyFGbRationalParametrization` Warning, `gb` is implicitly declared local to procedure `MyFGbRationalParametrization` Warning, `boo` is implicitly declared local to procedure `MyFGbRationalParametrization` Warning, `i` is implicitly declared local to procedure `MyFGbRationalParametrization` Warning, `candidate` is implicitly declared local to procedure `MyFGbRationalParametrization` Warning, `rr1` is implicitly declared local to procedure `MyFGbRationalParametrization` Warning, `DEG` is implicitly declared local to procedure `MyFGbRationalParametrization` Warning, `NEWVARS` is implicitly declared local to procedure `MyFGbRationalParametrization` Warning, `LS` is implicitly declared local to procedure `MyFGbRationalParametrization` Warning, `param` is implicitly declared local to procedure `MyFGbRationalParametrization` Warning, `out` is implicitly declared local to procedure `HowManyOnTheSpectra` Warning, `n` is implicitly declared local to procedure `HowManyOnTheSpectra` Warning, `pos` is implicitly declared local to procedure `HowManyOnTheSpectra` Warning, `i` is implicitly declared local to procedure `HowManyOnTheSpectra` Warning, `val` is implicitly declared local to procedure `HowManyOnTheSpectra` Warning, `j` is implicitly declared local to procedure `HowManyOnTheSpectra` Warning, `MAT` is implicitly declared local to procedure `HowManyOnTheSpectra` Warning, `v` is implicitly declared local to procedure `HowManyOnTheSpectra` Warning, `z` is implicitly declared local to procedure `HowManyOnTheSpectra` Warning, `out` is implicitly declared local to procedure `HowManyOnTheSpectraHankel` Warning, `n` is implicitly declared local to procedure `HowManyOnTheSpectraHankel` Warning, `pos` is implicitly declared local to procedure `HowManyOnTheSpectraHankel` Warning, `i` is implicitly declared local to procedure `HowManyOnTheSpectraHankel` Warning, `val` is implicitly declared local to procedure `HowManyOnTheSpectraHankel` Warning, `j` is implicitly declared local to procedure `HowManyOnTheSpectraHankel` Warning, `MAT` is implicitly declared local to procedure `HowManyOnTheSpectraHankel` Warning, `v` is implicitly declared local to procedure `HowManyOnTheSpectraHankel` Warning, `z` is implicitly declared local to procedure `HowManyOnTheSpectraHankel` Warning, `varsX` is implicitly declared local to procedure `RealSmallRankHankel` Warning, `matY` is implicitly declared local to procedure `RealSmallRankHankel` Warning, `s` is implicitly declared local to procedure `RealSmallRankHankel` Warning, `i` is implicitly declared local to procedure `RealSmallRankHankel` Warning, `varsY` is implicitly declared local to procedure `RealSmallRankHankel` Warning, `g` is implicitly declared local to procedure `RealSmallRankHankel` Warning, `BB` is implicitly declared local to procedure `RealSmallRankHankel` Warning, `NEWEQ` is implicitly declared local to procedure `RealSmallRankHankel` Warning, `j` is implicitly declared local to procedure `RealSmallRankHankel` Warning, `EQS` is implicitly declared local to procedure `RealSmallRankHankel` Warning, `varsXY` is implicitly declared local to procedure `RealSmallRankHankel` Warning, `st0` is implicitly declared local to procedure `RealSmallRankHankel` Warning, `times` is implicitly declared local to procedure `RealSmallRankHankel` Warning, `ldeg` is implicitly declared local to procedure `RealSmallRankHankel` Warning, `HYP` is implicitly declared local to procedure `RealSmallRankHankel` Warning, `SOLS` is implicitly declared local to procedure `RealSmallRankHankel` Warning, `deg` is implicitly declared local to procedure `RealSmallRankHankel` Warning, `myvar` is implicitly declared local to procedure `RealSmallRankHankel` Warning, `param` is implicitly declared local to procedure `RealSmallRankHankel` Warning, `chgvar` is implicitly declared local to procedure `RealSmallRankHankel` Warning, `st1` is implicitly declared local to procedure `RealSmallRankHankel` Warning, `NUMB` is implicitly declared local to procedure `RealSmallRankHankel` Warning, `varsZ` is implicitly declared local to procedure `OldLagSyst` Warning, `varsXY` is implicitly declared local to procedure `OldLagSyst` Warning, `NEWEQS` is implicitly declared local to procedure `OldLagSyst` Warning, `zz` is implicitly declared local to procedure `OldLagSyst` Warning, `GB` is implicitly declared local to procedure `OldLagSyst` Warning, `SOLS` is implicitly declared local to procedure `OldLagSyst` Warning, `param` is implicitly declared local to procedure `LagSyst` Warning, `chgvar` is implicitly declared local to procedure `LagSyst` Warning, `SOLS` is implicitly declared local to procedure `LagSyst` Warning, `varsZ` is implicitly declared local to procedure `LagSyst` Warning, `varsXY` is implicitly declared local to procedure `LagSyst` Warning, `rr` is implicitly declared local to procedure `LagSyst` Warning, `NEWEQS` is implicitly declared local to procedure `LagSyst` Warning, `zz` is implicitly declared local to procedure `LagSyst` Warning, `lv` is implicitly declared local to procedure `LagSyst` Warning, `ld` is implicitly declared local to procedure `LagSyst` Warning, `varsZ` is implicitly declared local to procedure `PolarVarieties` Warning, `varsXY` is implicitly declared local to procedure `PolarVarieties` Warning, `J` is implicitly declared local to procedure `PolarVarieties` Warning, `jac` is implicitly declared local to procedure `PolarVarieties` Warning, `i` is implicitly declared local to procedure `PolarVarieties` Warning, `j` is implicitly declared local to procedure `PolarVarieties` Warning, `NEWEQS` is implicitly declared local to procedure `PolarVarieties` Warning, `rr` is implicitly declared local to procedure `IsSingular` Warning, `lv` is implicitly declared local to procedure `IsSingular` Warning, `ld` is implicitly declared local to procedure `IsSingular` Warning, `NEWEQUATIONS` is implicitly declared local to procedure `IsSingular` Warning, `GB` is implicitly declared local to procedure `IsSingular` Warning, `NEWVARS` is implicitly declared local to procedure `IsSingularMohab` Warning, `VEC` is implicitly declared local to procedure `IsSingularMohab` Warning, `NEWVEC` is implicitly declared local to procedure `IsSingularMohab` Warning, `NEWPOLS` is implicitly declared local to procedure `IsSingularMohab` Warning, `NEWEQS` is implicitly declared local to procedure `IsSingularMohab` Warning, `GB` is implicitly declared local to procedure `IsSingularMohab` Warning, `n` is implicitly declared local to procedure `RealSmallRank` Warning, `varsX` is implicitly declared local to procedure `RealSmallRank` Warning, `matY2` is implicitly declared local to procedure `RealSmallRank` Warning, `i` is implicitly declared local to procedure `RealSmallRank` Warning, `j` is implicitly declared local to procedure `RealSmallRank` Warning, `U` is implicitly declared local to procedure `RealSmallRank` Warning, `matY1` is implicitly declared local to procedure `RealSmallRank` Warning, `matY` is implicitly declared local to procedure `RealSmallRank` Warning, `varsY` is implicitly declared local to procedure `RealSmallRank` Warning, `rr` is implicitly declared local to procedure `RealSmallRank` Warning, `EQS` is implicitly declared local to procedure `RealSmallRank` Warning, `varsXY` is implicitly declared local to procedure `RealSmallRank` Warning, `st` is implicitly declared local to procedure `RealSmallRank` Warning, `GB` is implicitly declared local to procedure `RealSmallRank` Warning, `param` is implicitly declared local to procedure `RealSmallRank` Warning, `deg` is implicitly declared local to procedure `RealSmallRank` Warning, `st0` is implicitly declared local to procedure `RealSmallRank` Warning, `times` is implicitly declared local to procedure `RealSmallRank` Warning, `HYP` is implicitly declared local to procedure `RealSmallRank` Warning, `SOLS` is implicitly declared local to procedure `RealSmallRank` Warning, `st1` is implicitly declared local to procedure `RealSmallRank` Warning, `ldeg` is implicitly declared local to procedure `RealSmallRank` Warning, `s` is implicitly declared local to procedure `RealSmallRank` Warning, `myvar` is implicitly declared local to procedure `RealSmallRank` Warning, `NUMB` is implicitly declared local to procedure `RealSmallRank` Warning, `varsX` is implicitly declared local to procedure `RealSmallRankOldGood` Warning, `U` is implicitly declared local to procedure `RealSmallRankOldGood` Warning, `matY` is implicitly declared local to procedure `RealSmallRankOldGood` Warning, `i` is implicitly declared local to procedure `RealSmallRankOldGood` Warning, `j` is implicitly declared local to procedure `RealSmallRankOldGood` Warning, `varsY` is implicitly declared local to procedure `RealSmallRankOldGood` Warning, `ID` is implicitly declared local to procedure `RealSmallRankOldGood` Warning, `EQS` is implicitly declared local to procedure `RealSmallRankOldGood` Warning, `varsXY` is implicitly declared local to procedure `RealSmallRankOldGood` Warning, `HYP` is implicitly declared local to procedure `RealSmallRankOldGood` Warning, `SOLS` is implicitly declared local to procedure `RealSmallRankOldGood` Warning, `s` is implicitly declared local to procedure `RealSmallRankOldGood` Warning, `myvar` is implicitly declared local to procedure `RealSmallRankOldGood` Warning, `NUMB` is implicitly declared local to procedure `RealSmallRankOldGood` Warning, `varsX` is implicitly declared local to procedure `RealSmallRankOld` Warning, `matY` is implicitly declared local to procedure `RealSmallRankOld` Warning, `i` is implicitly declared local to procedure `RealSmallRankOld` Warning, `j` is implicitly declared local to procedure `RealSmallRankOld` Warning, `varsY` is implicitly declared local to procedure `RealSmallRankOld` Warning, `EQS` is implicitly declared local to procedure `RealSmallRankOld` Warning, `varsXY` is implicitly declared local to procedure `RealSmallRankOld` Warning, `HYP` is implicitly declared local to procedure `RealSmallRankOld` Warning, `SOLS` is implicitly declared local to procedure `RealSmallRankOld` Warning, `s` is implicitly declared local to procedure `RealSmallRankOld` Warning, `myvar` is implicitly declared local to procedure `RealSmallRankOld` Warning, `NUMB` is implicitly declared local to procedure `RealSmallRankOld` Warning, `varsX` is implicitly declared local to procedure `RealSmallRankChange` Warning, `matY` is implicitly declared local to procedure `RealSmallRankChange` Warning, `i` is implicitly declared local to procedure `RealSmallRankChange` Warning, `j` is implicitly declared local to procedure `RealSmallRankChange` Warning, `varsY` is implicitly declared local to procedure `RealSmallRankChange` Warning, `EQS` is implicitly declared local to procedure `RealSmallRankChange` Warning, `varsXY` is implicitly declared local to procedure `RealSmallRankChange` Warning, `HYP` is implicitly declared local to procedure `RealSmallRankChange` Warning, `SOLS` is implicitly declared local to procedure `RealSmallRankChange` Warning, `myvar` is implicitly declared local to procedure `RealSmallRankChange` Warning, `varsX` is implicitly declared local to procedure `RealSmallRankWithoutControl` Warning, `matY` is implicitly declared local to procedure `RealSmallRankWithoutControl` Warning, `i` is implicitly declared local to procedure `RealSmallRankWithoutControl` Warning, `j` is implicitly declared local to procedure `RealSmallRankWithoutControl` Warning, `varsY` is implicitly declared local to procedure `RealSmallRankWithoutControl` Warning, `EQS` is implicitly declared local to procedure `RealSmallRankWithoutControl` Warning, `varsXY` is implicitly declared local to procedure `RealSmallRankWithoutControl` Warning, `HYP` is implicitly declared local to procedure `RealSmallRankWithoutControl` Warning, `SOLS` is implicitly declared local to procedure `RealSmallRankWithoutControl` Warning, `s` is implicitly declared local to procedure `RealSmallRankWithoutControl` Warning, `myvar` is implicitly declared local to procedure `RealSmallRankWithoutControl` Warning, `NUMB` is implicitly declared local to procedure `RealSmallRankWithoutControl` Warning, `varsX` is implicitly declared local to procedure `RealSmallRankSymmetric` Warning, `matY` is implicitly declared local to procedure `RealSmallRankSymmetric` Warning, `varsY` is implicitly declared local to procedure `RealSmallRankSymmetric` Warning, `i` is implicitly declared local to procedure `RealSmallRankSymmetric` Warning, `j` is implicitly declared local to procedure `RealSmallRankSymmetric` Warning, `J` is implicitly declared local to procedure `RealSmallRankSymmetric` Warning, `EQS` is implicitly declared local to procedure `RealSmallRankSymmetric` Warning, `varsXY` is implicitly declared local to procedure `RealSmallRankSymmetric` Warning, `NEW` is implicitly declared local to procedure `RealSmallRankSymmetric` Warning, `HYP` is implicitly declared local to procedure `RealSmallRankSymmetric` Warning, `SOLS` is implicitly declared local to procedure `RealSmallRankSymmetric` Warning, `s` is implicitly declared local to procedure `RealSmallRankSymmetric` Warning, `myvar` is implicitly declared local to procedure `RealSmallRankSymmetric` Warning, `NUMB` is implicitly declared local to procedure `RealSmallRankSymmetric` Warning, `varsX` is implicitly declared local to procedure `RealSmallRankSymmetricChange` Warning, `matY` is implicitly declared local to procedure `RealSmallRankSymmetricChange` Warning, `i` is implicitly declared local to procedure `RealSmallRankSymmetricChange` Warning, `j` is implicitly declared local to procedure `RealSmallRankSymmetricChange` Warning, `varsY` is implicitly declared local to procedure `RealSmallRankSymmetricChange` Warning, `J` is implicitly declared local to procedure `RealSmallRankSymmetricChange` Warning, `EQS` is implicitly declared local to procedure `RealSmallRankSymmetricChange` Warning, `varsXY` is implicitly declared local to procedure `RealSmallRankSymmetricChange` Warning, `HYP` is implicitly declared local to procedure `RealSmallRankSymmetricChange` Warning, `SOLS` is implicitly declared local to procedure `RealSmallRankSymmetricChange` Warning, `myvar` is implicitly declared local to procedure `RealSmallRankSymmetricChange` Warning, `NUMB` is implicitly declared local to procedure `RealSmallRankSymmetricChange` Warning, `varsX` is implicitly declared local to procedure `RealSmallRankSymmetricWithoutControl` Warning, `matY` is implicitly declared local to procedure `RealSmallRankSymmetricWithoutControl` Warning, `i` is implicitly declared local to procedure `RealSmallRankSymmetricWithoutControl` Warning, `j` is implicitly declared local to procedure `RealSmallRankSymmetricWithoutControl` Warning, `varsY` is implicitly declared local to procedure `RealSmallRankSymmetricWithoutControl` Warning, `J` is implicitly declared local to procedure `RealSmallRankSymmetricWithoutControl` Warning, `EQS` is implicitly declared local to procedure `RealSmallRankSymmetricWithoutControl` Warning, `varsXY` is implicitly declared local to procedure `RealSmallRankSymmetricWithoutControl` Warning, `HYP` is implicitly declared local to procedure `RealSmallRankSymmetricWithoutControl` Warning, `SOLS` is implicitly declared local to procedure `RealSmallRankSymmetricWithoutControl` Warning, `s` is implicitly declared local to procedure `RealSmallRankSymmetricWithoutControl` Warning, `myvar` is implicitly declared local to procedure `RealSmallRankSymmetricWithoutControl` Warning, `NUMB` is implicitly declared local to procedure `RealSmallRankSymmetricWithoutControl` Warning, `varsX` is implicitly declared local to procedure `RealSmallRankDiagonal` Warning, `matY` is implicitly declared local to procedure `RealSmallRankDiagonal` Warning, `i` is implicitly declared local to procedure `RealSmallRankDiagonal` Warning, `j` is implicitly declared local to procedure `RealSmallRankDiagonal` Warning, `varsY` is implicitly declared local to procedure `RealSmallRankDiagonal` Warning, `J` is implicitly declared local to procedure `RealSmallRankDiagonal` Warning, `EQS` is implicitly declared local to procedure `RealSmallRankDiagonal` Warning, `varsXY` is implicitly declared local to procedure `RealSmallRankDiagonal` Warning, `HYP` is implicitly declared local to procedure `RealSmallRankDiagonal` Warning, `SOLS` is implicitly declared local to procedure `RealSmallRankDiagonal` Warning, `s` is implicitly declared local to procedure `RealSmallRankDiagonal` Warning, `myvar` is implicitly declared local to procedure `RealSmallRankDiagonal` Warning, `NUMB` is implicitly declared local to procedure `RealSmallRankDiagonal` Warning, `varsX` is implicitly declared local to procedure `RealSmallRankOtherMinor` Warning, `matY` is implicitly declared local to procedure `RealSmallRankOtherMinor` Warning, `i` is implicitly declared local to procedure `RealSmallRankOtherMinor` Warning, `j` is implicitly declared local to procedure `RealSmallRankOtherMinor` Warning, `varsY` is implicitly declared local to procedure `RealSmallRankOtherMinor` Warning, `EQS` is implicitly declared local to procedure `RealSmallRankOtherMinor` Warning, `varsXY` is implicitly declared local to procedure `RealSmallRankOtherMinor` Warning, `HYP` is implicitly declared local to procedure `RealSmallRankOtherMinor` Warning, `SOLS` is implicitly declared local to procedure `RealSmallRankOtherMinor` Warning, `s` is implicitly declared local to procedure `RealSmallRankOtherMinor` Warning, `myvar` is implicitly declared local to procedure `RealSmallRankOtherMinor` Warning, `NUMB` is implicitly declared local to procedure `RealSmallRankOtherMinor` Warning, `varsX` is implicitly declared local to procedure `RealSmallRank2` Warning, `matY` is implicitly declared local to procedure `RealSmallRank2` Warning, `i` is implicitly declared local to procedure `RealSmallRank2` Warning, `j` is implicitly declared local to procedure `RealSmallRank2` Warning, `varsY` is implicitly declared local to procedure `RealSmallRank2` Warning, `EQS` is implicitly declared local to procedure `RealSmallRank2` Warning, `varsXY` is implicitly declared local to procedure `RealSmallRank2` Warning, `HYP` is implicitly declared local to procedure `RealSmallRank2` Warning, `SOLS` is implicitly declared local to procedure `RealSmallRank2` Warning, `myvar` is implicitly declared local to procedure `RealSmallRank2` Warning, `NUMB` is implicitly declared local to procedure `RealSmallRank2` Warning, `fd` is implicitly declared local to procedure `PrintFiles` Warning, `N` is implicitly declared local to procedure `GenerateHankelMatrix` Warning, `varsXX` is implicitly declared local to procedure `GenerateHankelMatrix` Warning, `VV` is implicitly declared local to procedure `GenerateHankelMatrix` Warning, `i` is implicitly declared local to procedure `GenerateHankelMatrix` Warning, `M` is implicitly declared local to procedure `GenerateHankelMatrix` Warning, `s` is implicitly declared local to procedure `GenerateHankelMatrix` Warning, `j` is implicitly declared local to procedure `GenerateHankelMatrix` Warning, `varsXX` is implicitly declared local to procedure `MyGenerateMatrix` Warning, `M` is implicitly declared local to procedure `MyGenerateMatrix` Warning, `i` is implicitly declared local to procedure `MyGenerateMatrix` Warning, `j` is implicitly declared local to procedure `MyGenerateMatrix` Warning, `r` is implicitly declared local to procedure `GenerateFilesHankel` Warning, `script1` is implicitly declared local to procedure `GenerateFilesHankel` Warning, `fd1` is implicitly declared local to procedure `GenerateFilesHankel` Warning, `script2` is implicitly declared local to procedure `GenerateFilesHankel` Warning, `fd2` is implicitly declared local to procedure `GenerateFilesHankel` Warning, `n` is implicitly declared local to procedure `GenerateFilesHankel` Warning, `M` is implicitly declared local to procedure `GenerateFilesHankel` Warning, `F` is implicitly declared local to procedure `GenerateFilesHankel` Warning, `str1` is implicitly declared local to procedure `GenerateFilesHankel` Warning, `logstr1` is implicitly declared local to procedure `GenerateFilesHankel` Warning, `varsXX` is implicitly declared local to procedure `GenerateFilesHankel` Warning, `str2` is implicitly declared local to procedure `GenerateFilesHankel` Warning, `logstr2` is implicitly declared local to procedure `GenerateFilesHankel` Warning, `M` is implicitly declared local to procedure `GenerateSingleFileHankel` Warning, `F` is implicitly declared local to procedure `GenerateSingleFileHankel` Warning, `str1` is implicitly declared local to procedure `GenerateSingleFileHankel` Warning, `varsXX` is implicitly declared local to procedure `GenerateSingleFileHankel` Warning, `str2` is implicitly declared local to procedure `GenerateSingleFileHankel` Warning, `script1` is implicitly declared local to procedure `GenerateFiles` Warning, `script2` is implicitly declared local to procedure `GenerateFiles` Warning, `F` is implicitly declared local to procedure `GenerateFiles` Warning, `str1` is implicitly declared local to procedure `GenerateFiles` Warning, `logstr1` is implicitly declared local to procedure `GenerateFiles` Warning, `varsXX` is implicitly declared local to procedure `GenerateFiles` Warning, `str2` is implicitly declared local to procedure `GenerateFiles` Warning, `logstr2` is implicitly declared local to procedure `GenerateFiles` Warning, `M` is implicitly declared local to procedure `GenerateSingleFile` Warning, `F` is implicitly declared local to procedure `GenerateSingleFile` Warning, `str1` is implicitly declared local to procedure `GenerateSingleFile` Warning, `varsXX` is implicitly declared local to procedure `GenerateSingleFile` Warning, `str2` is implicitly declared local to procedure `GenerateSingleFile` > > st:=time():RealSmallRank(Matrix(5, 5, [[8+100*X1+173*X2,49-195*X1+94*X2,43+99*X1+22*X2,-76-2*X1+40*X2,85+79*X1+49*X2],[24+85*X1-76*X2,80+84*X2,-16-156*X1+104*X2,58+36*X1-35*X2,2+8*X1-30*X2],[-44-92*X1-75*X2,-124+25*X1-92*X2,192+227*X1-140*X2,-43-141*X1+13*X2,-13-98*X1+49*X2],[43-97*X1+123*X2,148+54*X1+13*X2,280-69*X1+15*X2,147+7*X1+150*X2,70-181*X1-139*X2],[200+71*X1+207*X2,162+2*X1-6*X2,-159-74*X1+133*X2,-153+109*X1-65*X2,110-185*X1+100*X2]]), 5, [X1, X2], 2):lprint(time()-st): [-2 - 10 Y11 - 9 Y21 -63 - 10 Y12 - 9 Y22 48 - 10 Y13 - 9 Y23] [ ] [16 - 5 Y11 - 7 Y21 -93 - 5 Y12 - 7 Y22 -2 - 5 Y13 - 7 Y23 ] [ ] [-14 - 7 Y11 - 2 Y21 -21 - 7 Y12 - 2 Y22 -55 - 7 Y13 - 2 Y23] [ ] [ Y11 Y12 Y13 ] [ ] [ Y21 Y22 Y23 ] Set tr to 1 INCREASE HEAP 14470848 [2](15x21)100%/[2](21x24)100%/[2](19x15)100%/ #C Dimension: -1, Degree: -1 Elapsed time (empty case): 0.028000 .48e-1 > quit memory used=6.7MB, alloc=40.3MB, time=0.17